Investigations in
Number, Data, and Space:
Teaching Philosophy
The Changing Face of
Mathematics Instruction:
What is different?
 New roles for teachers and students
 Teaching for understanding
 All children can learn
 Collaborative work
 Alternative and multiple strategies
Organization of the
Investigations Curriculum
 Units (2- 6 weeks) – consists of several
investigations on the same/similar topics
 Investigations several sessions around
A set of related problems
Math relationships – building/constructing
Games about particular mathematics
Collecting, representing and interpreting data
 Sessions – structure/learning cycle
 Extensions & Excursions - differentiation
Learning Cycle
ENGAGE (hook; prior knowledge)
EXPLORE (hands on; experience)
EXPLAIN (term introduction)
EXTEND (yet another way)
EVALUATE (are learners getting the
 If YES, …
 If NO, …
The Mathematics Content
Special Features of the
Investigations Curriculum
Cooperative learning and grouping
Family connections
Review and practice
Support for Spanish-speaking students
The Teacher’s Role
 Observe & listen carefully to students; Understand
how students are thinking
 Help students articulate their thinking, verbally & in
 Establish a classroom atmosphere in which high value
is placed on thinking hard about a problem
 Insist that students keep track of their work and be
able to explain or show their thinking
 Ask questions that push students’ mathematical
thinking further
 Facilitate discussions about important math ideas
 Make decisions about how to modify the curriculum
appropriately for individuals or groups of students
Differentiating Instruction:
Can we do it?
 Everybody Counts (NRC, 1989)
 Investigating real-life contexts
 Linguistically diverse classroom
 Spanish vocabulary package
 Tips for linguistically diverse classroom
 Family letters (in six languages)
 Investigating mathematical contexts
Differentiating Instruction:
Process standards
Problem solving
Reasoning and proof

Investigations in Number, Data, and Space: …